I was playing with a very old mint condition Leica M3 (The 2 winding one). I snapped a picture with no film in the camera, turned the lever twice, and tried again. After I tried a few times, it suddenly stopped snapping. I couldn't press the shutter down! I was very confused...

Anyways, I tried to fire off the timer, and it made a clicking noise, but I'm not sure if it was the shutter. I really don't want a Leica to be broken, it's such a good camera!

Anyways, I know that the majority of you don't own an M3, not even a Leica for that matter. But ANY help would be appreciated! I'm devastated!

I have a similar problem with an oldie my mom bought for decoration purposes, which isn't a Leica by the way. It uses a little switch to expose the film, and makes a nice silent click when opening. After firing a shot or three, however, it stops working. I'd say it's because the camera is so old, but it might be fixable. Especially on a Leica M3.
Fix for the shutter button on my old camera is to set the only other switch (there's only two ) from 'normal' to 'bright light' and then back again...

OH man, that sounds pants. I'd love an M3 but yeah suggestions above are a good start. I would like that rangefinder website more but it's so dark and unfriendly, plus it's also horribly set out. It just puts me off.